nLab Verschiebung morphism

(under construction)

Idea

The Verschiebung morphism (German for ‘shift’) is an endomorphism, related to the Frobenius morphism.

Witt vectors

For a commutative ring $A$, let $\mathbb{W}(A)$ denote the set $1+T A[[T]]$ of power series in $A$ with constant term one. Given a positive integer $n$, the Verschiebung homomorphism is the additive homomorphism $V_n : \mathbb{W}(A) \to \mathbb{W}(A)$ defined by the formula $V_n(f(T)) = f(T^n)$.